Utilization of geographically weighted regression for geoid modelling in Egypt

Modelling the spatial variations of a specific Global Geopotential Model (GGM) over a spatial area is important to enhance its local performance in Global Navigation Satellite Systems (GNSS) surveying. This study aims to investigate the potential of utilizing some of Geographic Information Systems (GIS) geospatial analysis tools, particularly Geographically Weighted Regression (GWR), in geoid modelling for the first time in Egypt as a case study. Its main target is developing an optimum regression method to be applied in spatial modelling of the deviations of a specific GGM (e.g., PGM17). Using a precise local geodetic dataset of 803 GPS/levelling stations, PGM17 undulation differences have been modelled using different regression techniques to evaluate their precision and accuracy. Based on investigating 13 possible regression formulas of probable combinations of independent variables, results showed that the PGM17 discrepancies over Egypt depend mostly on the terrain heights and geoidal undulations. Over 80 checkpoints, the attained variations between the GWR model and known values varied from -0.574 m to 0.500 m, with a mean of 0.001 m and a standard deviation equals +/- 0.205 m. Based on available data, it has been found that GWR improved the PGM17 deviations by 9 % in terms of standard deviation and by 98 % in terms of the mean. Additionally, the study generates a reasonably innovative product for the local geodetic community by building an enhanced version of the PGM17. This surface will be a precious resource in GNSS surveying in Egypt for heights conversion, leading to considerable cost reduction in civil engineering works and mapping projects.